Corpus ID: 237940705

The geometric field of linearity of linear sets

  title={The geometric field of linearity of linear sets},
  author={Dibyayoti Jena and Geertrui Van de Voorde},
If an Fq-linear set LU in a projective space is defined by a vector subspace U which is linear over a proper superfield of Fq, then all of its points have weight at least 2. It is known that the converse of this statement holds for linear sets of rank h in PG(1, q) but for linear sets of rank k < h, the converse of this statement is in general no longer true. The first part of this paper studies the relation between the weights of points and the size of a linear set, and introduces the concept… Expand


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  • Simeon Ball
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. A
  • 2003
A proof is presented that shows that the number of directions determined by a function over a finite field GF(q) is either 1, at least (q + 3)/2, or between q/s + 1 and (q - 1)/(s - 1) for some sExpand
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